“Cambridge was always my dream,” says 17-year-old Hridita Rahman Khan, one of 41 students at Brampton Manor academy in east London to have won offers from Oxbridge this week.

Khan’s parents are from Bangladesh, she grew up in Italy and arrived in London at the age of 14 with little English. Three years later she has been offered a place to study engineering at the University of Cambridge.

Her story is one of extraordinary achievement, but there are many at Brampton Manor, a state school in Newham where half of those holding Oxbridge offers are on free school meals and nearly all are from minority ethnic backgrounds.

Dorcas Shodeinde, 17, was put into care at the age of 14. “I was really scared. I looked at the statistics for children in care and a lot of people don’t do well,” she says. If she achieves the required A-levels, she’s off to study law at Oxford. “At the moment it doesn’t feel real.”

Brampton Manor may be located in one of the poorest boroughs in London but its success now rivals that of some of the top private schools across the country. By way of comparison, in 2015 68 students from Eton College were accepted by Oxbridge, out of a cohort of 267.

A key factor in the success is that although the school (for ages 11-16) is comprehensive, the sixth form is highly selective. It opened in 2012 and attracts up to 3,000 applications for 300 places each year. Some of its students travel up to two hours each way to attend.

Each candidate is interviewed and, according to the director of sixth form, Sam Dobin, most of those who are successful average the equivalent of A grades at GCSE.

Of the 300-plus pupils in year 11 at Brampton Manor, about 70 continue into the sixth form. Of the 41 Oxbridge offers, nine are from the school’s own comprehensive intake, which is more in keeping with outcomes at other high-achieving schools around the country.

Another contributing factor is the high number of students who apply to Oxbridge. While other school sixth forms lack ambition and might enter a handful of students, 130 applied from Brampton Manor this year and Dobin says he believes every single one of his current year 12 is capable of going to Oxbridge. “This is not a fluke. We will have more next year. The secret is having the students believe in themselves.”

Visually, Brampton Manor resembles any number of modern academies. It’s bigger than most with 2,500 students, of which just 2% are of white British origin.

The walls are plastered with photographs of success stories, and in the entrance to the sixth form there are honours boards listing previous students’ names and the university to which they went. There’s a separate board for Oxbridge, the names topped by the school’s first Oxbridge student, Nulifa Ahmed, who went on to get a first in geography at Cambridge.

The academy has no links with top private schools, unlike its more famous Newham neighbour the London Academy of Excellence (LAE), another selective sixth form, which was set up as part of Conservatives’ free schools programme and is supported by a number of independent schools including Eton.

Nor has it cultivated relationships with individual Oxbridge colleges. Dobin says its success has nothing to do with “inside knowledge”. Instead, he says, students excel through their own hard work and ambition, supported by highly qualified staff.

There is a university access team made up of five Oxbridge graduates who are not teachers and are there solely to support university applications, including giving mock interviews.

Each student has three or four hours of lessons a day. “In free periods we don’t release them to go to town to go to Nando’s,” says Dobin, who graduated from Cambridge. They are expected to stay on site and work, and in the sixth form study area row upon row of students sit in silence, heads in books. The study area is open from 6am to 6pm and Dobin says there are students who are regularly there for the full 12 hours.

The executive principal, Dayo Olukoshi, is delighted for the 41 offer holders. He regards himself and his team as “missionaries” and tells students: “It’s not about the way you look. It’s not about your skin colour or whether you fit in or not. It’s about – how ambitious are you? How big is your dream? Because we are in the business of bringing your dreams into reality.”

The school’s success has won plaudits from far and wide, including another near neighbour, Newham Sixth Form College (NewVic), a traditional, comprehensive sixth form, which arguably loses high-achieving students to Brampton Manor, LAE and the selective Newham Collegiate.

NewVic’s principal, Mandeep Gill, said he was delighted at Brampton Manor’s success but warned against fetishising Oxbridge as the pinnacle of achievement.

“I’m really proud of what Brampton Manor has achieved. What they’ve done for those students is fantastic. But I am very much in favour of giving every student every opportunity to achieve on their terms,” he said.

“For some students that’s Oxford and Cambridge, and that’s brilliant, but for many others it’s not. As a college we do both ends. We send students to Oxford and Cambridge, but we also celebrate and are just as proud of those 70 students who got apprenticeships last year.”

James Turner, the incoming chief executive of the Sutton Trust, a social mobility charity, paid tribute to Brampton Manor’s success.

“The key thing from our point of view is that these schools continue to serve their neighbourhoods. As the school becomes more desirable, competition to get in to the sixth form may become more intense,” he said.

“If that’s the case, it’s important the school makes sure it continues to fulfil the mission it was set up to fulfil.”